Why is a small sample size not enough?

Background: Clinical studies are often limited by resources available, which results in constraints on sample size. We use simulated data to illustrate study implications when the sample size is too small.

Methods And Results: Using 2 theoretical populations each with N = 1000, we randomly sample 10 from each population and conduct a statistical comparison, to help make a conclusion about whether the 2 populations are different. This exercise is repeated for a total of 4 studies: 2 concluded that the 2 populations are statistically significantly different, while 2 showed no statistically significant difference.

Conclusions: Our simulated examples demonstrate that sample sizes play important roles in clinical research. The results and conclusions, in terms of estimates of means, medians, Pearson correlations, chi-square test, and P values, are unreliable with small samples.